The invention relates to the display of information in an aircraft cockpit. Modern aircraft, in particular transport planes, generally comprise a system for displaying flight assistance information in their cockpit. Such a system, for example of the CDS (for Control and Display System) type controls the display of information on screens, referred to as head down displays, of the cockpit. Usually, these screens are provided for displaying primary flight information of the aircraft, navigation information, etc. In order to allow the user to see a display of information without being constrained to lower his/her head to look at the screens, some aircraft are now equipped with a head up display device, commonly referred to as a HUD, for Head Up Display, and/or of a device configured so as to be worn rigidly attached to the head of the user. Such a device is commonly referred to as a HMD, for Head Mounted Display. It is sometimes also referred to as a HWD, for Head Worn Display. It generally comprises a display unit rigidly mounted onto glasses or a helmet, in such a manner that the user can see information displayed on the display unit when they are wearing these glasses or this helmet. In the following part of the description, the term HMD denotes both a HMD device and a HWD device. Furthermore, the pilots of aircraft often dispose of a device of the EFB (for Electronic Flight Bag) type external to the avionics systems of the aircraft, allowing them to use software applications not certified by the aeronautics certification authorities. According to a first alternative, this device of the EFB type corresponds to a computer integrated into the aircraft, whose display is generally formed on a screen integrated into the cockpit. The integration of a screen into the cockpit is sometimes difficult because the space available in an aircraft cockpit for integrating a display screen is generally very limited. Moreover, the mass of the display screen leads to an increase in the mass of the aircraft. According to a second alternative, this device of the EFB type corresponds to a portable computer or to a tablet that the pilot can bring with him/her into the cockpit of the aircraft. According to a first variant, the device of the EFB type is then connected to a display screen integrated into the cockpit, which poses the same problems as those mentioned with reference to the first alternative. According to a second variant, the pilot uses directly a screen of the device of the EFB type. However, the screen of the device of the EFB type sometimes has a more reduced size than that of a screen in the cockpit, which limits the comfort of use, in particular for the manipulation of navigation maps. Moreover, the use of the device of the EFB type then requires the presence in the cockpit, near to the pilot, of a surface or of a support allowing this device of the EFB type to be placed or hung up. The integration of such a surface or such a support in the cockpit is sometimes difficult because the space available in a cockpit, near to the pilot, is generally very limited. There accordingly exists the need for a solution allowing an additional display to be integrated into the cockpit.